Problem: Ben is $4$ times as old as Ishaan. $6$ years ago, Ben was $6$ times as old as Ishaan. How old is Ben now?
Solution: We can use the given information to write down two equations that describe the ages of Ben and Ishaan. Let Ben's current age be $b$ and Ishaan's current age be $i$. The information in the first sentence can be expressed in the following equation: ${b = 4i}$ Six years ago, Ben was $b - 6$ years old, and Ishaan was $i - 6$ years old. The information in the second sentence can be expressed in the following equation: ${b - 6 = 6(i - 6)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$, it might be easiest to solve our first equation for $i$ and substitute it into our second equation. Solving our first equation for $i$, we get: ${i = \dfrac{b}{4}}$. Substituting this into our second equation, we get: $ {b - 6 = 6 (}{\frac{b}{4}} {- 6)} $ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 6 = \dfrac{3}{2} b - 36$. Solving for $b$, we get: $\dfrac{1}{2} b = 30$. $b = 2 \cdot 30 = 60$.